Keywords:

M-estimators;

outliers;

Huber's minimax result;

influence function;

breakdown point

Abstract

That the conclusion based on a data analysis be robust and stable is not merely a desirable feature, it is essential. To merit this quality label, a conclusion must be supported by strong data-based evidence and not simply be a discovery gleaned from a preconceived model and weakly supported by a part of the data. Robustness in statistics refers to the definition and investigation of procedures that lead to such stability. This article gives a brief overview of the concepts and procedures that are relevant in judging robustness. These have mostly been developed over the last five decades. WIREs Comp Stat 2011 3 85–94 DOI: 10.1002/wics.144

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